These are really philosophical questions. Asking why F=ma is like asking why the universe exists. Nobody really knows and probably never will. Newton's second law (F = ma) is the result of observation about how objects interact with one another. Mass is a property of an object that is related to the stuff from which it is made. People are still trying to figure out exactly what it is. What we do know is that there are many things that double when you double the amount of a substance, and triple if you triple the amount and so on. The amount of heat required to melt ice doubles if you double the amount of ice. The amount of effort you have to exert to lift a cube of ice doubles if you double the volume of the ice, etc., etc.

You can search the internet for definitions of mass, and based on the fact that you are even asking the question I suspect none of them will be satisfying to you. The defintions will probably all seem circular, talking about resistance to changes in motion, which is just a vague way of saying that something like F = ma is at work without saying exactly what the relationship is.

Why F = ma? For the simple reason that it works. While the definitions of force and mass may seem to be circular, the fact is that this equation gives a self consistent way of analyzing the interactions among the many lumps of matter that make up the universe.